Covic made his A-League debut in a 3–2 loss to Adelaide United in December 2006 at Hindmarsh Stadium. Čović was the starting goalkeeper for Newcastle Jets in the 2007 season which he won the A-League championship. On 17 March 2009, it was announced that Covic was leaving the Jets for a three-year deal with Swedish club IF Elfsborg.

On 4 October 2011, Covic signed a one-year deal with Melbourne Victory as an injury replacement for Tando Velaphi who was ruled out for 12 weeks. Čović debuted in the opening game for the A-League season against Sydney FC at Etihad Stadium in front of 40,000 in attendance. Covic achieved instant hero status with the home fans when he thwarted Emerton from the penalty spot in the 33rd minute, he was named man of the match in the 0–0 draw. He was again named man of the match after the Melbourne Derby two weeks later.

In the A-League round 5 match between Brisbane Roar and Melbourne Victory in 2011, Covic, along with fellow Victory defender Matthew Foschini, were controversially sent off by referee Ben Williams for challenges against Roar defenders, reducing the Victory to playing with nine men throughout the match.[1]

On 1 May 2012, it was announced new Melbourne Victory coach Ange Postecoglou would not resign the veteran goalkeeper, opting to stay with younger goalkeepers Lawrence Thomas and Tando Velaphi. The shock decision came after Covic was awarded the Player's Player of the Year award at the Melbourne Victory Awards Dinner.

On 2 July 2012, Covic joined A-League expansion club Western Sydney Wanderers on a free transfer.[2] The Wanderers performed above expectations and won the Premier's Plate in their maiden season,[3] with Čović being named in the inaugural A-League All-Star team.[4] He helped his side to win 2014AFC Champions League, with keeping 8 clean sheets in 12 matches. At the end of the final which they defeated Al-Hilal, he was named as MVP of the tournament.

He made his debut for Australia against Bahrain on 22 February 2006 in an Asian Cup qualifier. On 22 March 2008 he earned his second cap against Singapore in an international friendly and was captain for part of the second half after Harry Kewell and Jade North left the field. As of 2014, Čović has two international caps with Australia.